A comparison of two methods for deriving bounds on the effective conductivity of composites

Abstract

An infinite set of bounds on the effective conductivity σe of a two-component composite has previously been derived using the analytic properties ofσc as a function of σ1 and σ2 (the conductivities of the components). We show that this same set of bounds can alternatively be derived from variational principles. The bounds incorporate information about the microstructure of the composite in addition to the volume fractions of the components.